The present invention relates to prism optical systems including a reflecting surface that is decentered and has a power, for example, a prism optical system for use in an image-forming optical system, a finder optical system, etc. used in cameras, video cameras and so forth.
Recently, there have been proposed optical systems designed to be compact in size by giving a power to a reflecting surface and folding an optical path in the direction of the optical axis. In such optical systems, a prism or a mirror is mainly used as a member having a reflecting surface with a power. An optical system having a prism and an optical system having a mirror are largely different in characteristics from each other although these optical systems are the same in terms of the structure using a reflecting surface.
When a curvature (radius r of curvature) is given to a reflecting surface of a prism and to a reflecting surface of a mirror, the power of each of the reflecting surfaces is given by the paraxial power calculating equation as follows. The power of the reflecting surface of the prism is xe2x88x922n/r in a case where the prism is filled therein with a medium having a refractive index n larger than 1, whereas the power of the reflecting surface of the mirror is xe2x88x922/r. Thus, even when these reflecting surfaces have the same curvature, the powers are different from each other. Accordingly, the curvature required for the prism is 1/n of the curvature required for the mirror to obtain the same power. Therefore, the prism produces a smaller amount of aberration at the reflecting surface than in the case of the mirror. Thus, the prism is more favorable than the mirror in terms of performance. Moreover, the prism has two refracting surfaces, i.e. an entrance refracting surface and an exit refracting surface, in addition to a reflecting surface as a single member. Therefore, the prism is advantageous from the viewpoint of aberration correction in comparison to the mirror, which has only a reflecting surface as a single member. Furthermore, because the prism is filled with a medium having a refractive index larger than 1, it is possible to obtain a longer optical path length than in the case of the mirror, which is placed in the air. Accordingly, it is relatively easy with the prism to provide the required reflecting surface even when the focal length is short. In general, reflecting surfaces require a high degree of accuracy for assembly because decentration errors of reflecting surfaces cause the performance to be degraded to a considerable extent in comparison to refracting surfaces. In a case where an optical system is constructed by arranging a plurality of reflecting surfaces, the prism is more advantageous than the mirror because the prism enables a plurality of reflecting surfaces to be integrated into one unit so as to fix the relative positions and is therefore capable of preventing performance degradation due to assembling. Thus, the prism is superior to the mirror in many respects.
Meanwhile, when a surface with a power is placed at a tilt to the optical axis, rotationally asymmetric aberrations are produced. For example, if a rotationally asymmetric distortion occurs, a square object may become trapezoidal undesirably. Such rotationally asymmetric aberrations (hereinafter referred to as xe2x80x9cdecentration aberrationsxe2x80x9d) are impossible to correct by a rotationally symmetric surface in theory. For this reason, rotationally asymmetric curved surfaces, e.g. anamorphic surfaces, are used in conventional prism optical systems.
Such prism optical systems include the disclosure of Japanese Patent Application Unexamined Publication (KOKAI) Number [hereinafter referred to as xe2x80x9cJP(A)xe2x80x9d] 8-313829. JP(A) 8-313829 discloses an ocular optical system comprising a prism in which there are two reflections, and a first transmitting surface and a second reflecting surface, as counted from the pupil side, are formed from the identical surface. In this optical system, all reflecting surfaces are rotationally asymmetric anamorphic surfaces.
Among the conventional prism optical systems using rotationally asymmetric curved surfaces, prism optical systems in which there are four reflections, in particular, are disclosed in JP(A) 8-292372, 9-73043, 9-197336 and 10-161018.
JP(A) 8-292372 discloses a zoom optical system in which a second reflecting surface and a first transmitting surface, as counted from the object side, are formed from the identical surface, and a third reflecting surface and a second transmitting surface, as counted from the object side, are formed from the identical surface. A first reflecting surface and a fourth reflecting surface are formed independently of the other transmitting surfaces and reflecting surfaces. The first and fourth reflecting surfaces are rotationally asymmetric surfaces, but the second and third reflecting surfaces are plane surfaces, which have no power. The zoom optical system is arranged to form an image once in the prism in order to relay the image.
Example 9 of JP(A) 9-73043 is an ocular optical system formed from a prism in which a first reflecting surface and a third reflecting surfaces, as counted from the pupil side, are formed from the identical surface with a second transmitting surface, and two other reflecting surfaces, i.e. second and fourth reflecting surfaces, are formed independently of the other transmitting surfaces and reflecting surfaces. The first, second and third reflecting surfaces are rotationally asymmetric anamorphic surfaces.
Example 3 of JP(A) 9-197336 is an ocular optical system formed from a prism in which a second reflecting surface and a fourth reflecting surface, as counted from the pupil side, are formed from the identical surface with a first transmitting surface, and a third reflecting surface is formed from the identical surface with a second transmitting surface. Only one reflecting surface, i.e. a first reflecting surface, is formed independently of the other transmitting surfaces and reflecting surfaces. All the reflecting surfaces are rotationally asymmetric anamorphic surfaces.
Example 21 of JP(A) 10-161018 is an optical system formed from a prism in which a second reflecting surface is formed from the identical surface with a first transmitting surface, and a third reflecting surface is formed from the identical surface with a second transmitting surface. Two other reflecting surfaces, i.e. first and fourth reflecting surfaces are formed independently of the other transmitting surfaces and reflecting surfaces. However, no numerical example is shown, and no detailed arrangement is mentioned.
These prior art prism optical systems suffer, however, from various problems as stated below.
In JP(A) 8-313829, because the prism optical system has only two reflecting surfaces, there is a limit in achieving high performance even if the prism reflecting surfaces are formed into rotationally asymmetric surfaces. Therefore, if the aperture becomes large or the field angle becomes large, the optical system may fail to fulfill the required high performance.
Accordingly, it is conceivable to increase the number of reflections so that aberration correction can be made satisfactorily even in the above case. However, high performance cannot always be attained in the prior art prism optical system even if the number of reflections is increased.
In JP(A) 8-292372, there are four reflections. However, there are only two reflecting surfaces having a power. The other two reflecting surfaces are formed from plane surfaces, which have no aberration correcting effects. Accordingly, JP(A) 8-292372 is not substantially different in performance from a prism in which there are two reflections. Moreover, because an image is formed once in the optical path, the powers of the surfaces need to be increased. This results in an increase in the amount of aberration produced. It is difficult to fulfill the required performance satisfactorily unless a large number of reflecting surfaces are used. In addition, because the image is relayed, the optical path length becomes long, and the prism tends to become large in size.
In Example 9 of JP(A) 9-73043, all the reflecting surfaces are given a power. However, the first and third reflecting surfaces are formed from the identical surface with the second transmitting surface. Therefore, the angle of reflection at each of the first and third reflecting surfaces needs to be larger than the total reflection critical angle (critical angle) in order to effect total reflection. In addition, to allow light to be totally reflected at the first and third reflecting surfaces, which are formed from the identical surface, it is necessary to increase the reflection angle at the second reflecting surface, which is placed between the first and third reflecting surfaces. For this reason, despite the arrangement using four reflecting surfaces, it is difficult to effect aberration correction satisfactorily because it is necessary to increase the reflection angles at three of the four reflecting surfaces.
In Example 3 of JP(A) 9-197336 also, the second and fourth reflecting surfaces are formed from the identical surface with the first transmitting surface, and the third reflecting surface is formed from the identical surface with the second transmitting surface. Therefore, there are restrictions on the reflection angles at three of the four reflecting surfaces. Accordingly, it is difficult to effect aberration correction satisfactorily.
In Example 21 of JP(A) 10-161018, the arrangement of an optical system is described, but no consideration is given to the performance aspect. Accordingly, the optical system lacks feasibility.
Thus, all the prior art prism optical systems involve problems in terms of performance in particular. There has heretofore been no compact and high-performance prism optical system that satisfies the demand for an improvement in performance and the demand for a reduction in size at the same time.
In view of the above-described problems associated with the prior art, an object of the present invention is to provide a compact and high-performance prism optical system.
A prism optical system according to a first aspect of the present invention provided to attain the above-described object has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, a fourth reflecting surface, and a second transmitting surface. The first transmitting surface and the second reflecting surface are formed from the identical surface, and the second transmitting surface and the third reflecting surface are formed from the identical surface. The first reflecting surface and the fourth reflecting surface are formed from surfaces independent of the first and second transmitting surfaces. At least one of the reflecting surfaces is formed from a rotationally asymmetric surface. At least one of the second and third reflecting surfaces has a power.
A prism optical system according to a second aspect of the present invention provided to attain the above-described object has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, a fourth reflecting surface, and a second transmitting surface. The first transmitting surface and the second reflecting surface are formed from the identical surface, and the second transmitting surface and the third reflecting surface are formed from the identical surface. The first and fourth reflecting surfaces are formed from surfaces independent of the first and second transmitting surfaces. At least one of the reflecting surfaces is formed from a rotationally asymmetric surface. Light rays from an object form an image only after passing through the second transmitting surface without forming an intermediate image in the prism.
A prism optical system according to a third aspect of the present invention provided to attain the above-described object has, in order in which light rays pass from the object side, a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, a fourth reflecting surface, and a second transmitting surface. The first transmitting surface and the second reflecting surface are formed from the identical surface, and the second transmitting surface and the third reflecting surface are formed from the identical surface. The first and fourth reflecting surfaces are formed from surfaces independent of the first and second transmitting surfaces. At least one of the reflecting surfaces is formed from a rotationally asymmetric surface. Light rays from an object lead a virtual image to the position of an observer""s eyeball only after passing through the second transmitting surface without forming an intermediate image in the prism.
First, the reasons for adopting the above-described arrangement in the prism optical system according to the first aspect of the present invention, together with the function thereof, will be described below. As has been stated in regard to the prior art, if a reflecting surface is tilted with respect to the optical axis, rotationally asymmetric decentration aberrations are produced. Therefore, it is desirable that at least one reflecting surface of the surfaces used in the present invention should be a rotationally asymmetric surface. If a rotationally asymmetric surface is used as at least one reflecting surface, it becomes possible to correct the rotationally asymmetric decentration aberrations.
Let us explain the definition of a decentered system.
First, a coordinate system used in the following description and rotationally asymmetric surfaces will be described.
When a light ray from the object center that passes through the center of the stop and reaches the center of the image plane is defined as an axial principal ray, an optical axis defined by a straight line along which the axial principal ray travels until it intersects the first surface of the optical system is defined as a Z-axis. An axis perpendicularly intersecting the Z-axis in the decentration plane of each surface constituting the prism optical system is defined as a Y-axis. An axis perpendicularly intersecting the optical axis and also perpendicularly intersecting the Y-axis is defined as an X-axis. In the following description, ray tracing is forward ray tracing in which rays are traced from the object toward the image plane.
The rotationally asymmetric surface used in the present invention should preferably be a plane-symmetry free-form surface having only one plane of symmetry.
Free-form surfaces used in the present invention are defined by the following equation (A).                     Z        =                                            C              2                        ⁢            X                    +                                    C              3                        ⁢            Y                    +                                    C              4                        ⁢                          X              2                                +                                    C              5                        ⁢            X            ⁢                          xe2x80x83                        ⁢            Y                    +                                    C              6                        ⁢                          Y              2                                +                                    C              7                        ⁢                          X              3                                +                                    C              8                        ⁢                          X              2                        ⁢            Y                    +                                    C              9                        ⁢            X            ⁢                          xe2x80x83                        ⁢                          Y              2                                +                                    C              10                        ⁢                          Y              3                                +                                    C              11                        ⁢                          X              4                                +                                    C              12                        ⁢                          X              3                        ⁢            Y                    +                                    C              13                        ⁢                          X              2                        ⁢                          Y              2                                +                                    C              14                        ⁢            X            ⁢                          xe2x80x83                        ⁢                          Y              3                                +                                    C              15                        ⁢                          Y              4                                +                                    C              16                        ⁢                          X              5                                +                                    C              17                        ⁢                          X              4                        ⁢            Y                    +                                    C              18                        ⁢                          X              3                        ⁢                          Y              2                                +                                    C              19                        ⁢                          X              2                        ⁢                          Y              3                                +                                    C              20                        ⁢            X            ⁢                          xe2x80x83                        ⁢                          Y              4                                +                                    C              21                        ⁢                          Y              5                                +                                    C              22                        ⁢                          X              6                                +                                    C              23                        ⁢                          X              5                        ⁢            Y                    +                                    C              24                        ⁢                          X              4                        ⁢                          Y              2                                +                                    C              25                        ⁢                          X              3                        ⁢                          Y              3                                +                                    C              26                        ⁢                          X              2                        ⁢                          Y              4                                +                                    C              27                        ⁢            X            ⁢                          xe2x80x83                        ⁢                          Y              5                                +                                    C              28                        ⁢                          Y              6                                +                                    C              29                        ⁢                          X              7                                +                                    C              30                        ⁢                          X              6                        ⁢            Y                    +                                    C              31                        ⁢                          X              5                        ⁢                          Y              2                                +                                    C              32                        ⁢                          X              4                        ⁢                          Y              3                                +                                    C              33                        ⁢                          X              3                        ⁢                          Y              4                                +                                    C              34                        ⁢                          X              2                        ⁢                          Y              5                                +                                    C              35                        ⁢            X            ⁢                          xe2x80x83                        ⁢                          Y              6                                +                                    C              36                        ⁢                          Y              7                                                          (        A        )            
In general, the above-described free-form surface does not have planes of symmetry in both the XZ- and YZ-planes. In the present invention, however, a free-form surface having only one plane of symmetry parallel to the YZ-plane is obtained by making all terms of odd-numbered degrees with respect to X zero. For example, in the above defining equation (A), the coefficients of the terms C2, C5, C7, C9, C12, C14, C16, C18, C20, C23, C25, C27, C29, C31, C33, C35, . . . are set equal to zero. By doing so, it is possible to obtain a free-form surface having only one plane of symmetry parallel to the YZ-plane.
A free-form surface having only one plane of symmetry parallel to the XZ-plane is obtained by making all terms of odd-numbered degrees with respect to Y zero. For example, in the above defining equation (A), the coefficients of the terms C3, C5, C8, C10, C12, C14, C17, C19, C21, C23, C25, C27, C30, C32, C34, C36, . . . are set equal to zero. By doing so, it is possible to obtain a free-form surface having only one plane of symmetry parallel to the XZ-plane.
Furthermore, the direction of decentration is determined in correspondence to either of the directions of the above-described planes of symmetry. For example, with respect to the plane of symmetry parallel to the YZ-plane, the direction of decentration of the optical system is determined to be the Y-axis direction. With respect to the plane of symmetry parallel to the XZ-plane, the direction of decentration of the optical system is determined to be the X-axis direction. By doing so, rotationally asymmetric aberrations due to decentration can be corrected effectively, and at the same time, productivity can be improved.
It should be noted that the above defining equation (A) is shown as merely an example, and that the feature of the present invention resides in that rotationally asymmetric aberrations due to decentration are corrected and, at the same time, productivity is improved by using a rotationally asymmetric surface having only one plane of symmetry. Therefore, the same advantageous effect can be obtained for any other defining equation that expresses such a rotationally asymmetric surface.
It becomes possible to correct decentration aberrations by using such a rotationally asymmetric surface. However, if the number of aberration correcting surfaces is small, the increase in performance is limited even if rotationally asymmetric surfaces are used. Therefore, increasing the number of reflecting surfaces of the prism optical system is deemed favorable from the viewpoint of performance. However, if the number of reflecting surfaces is increased by using a plurality of prisms, performance degradation is likely to occur owing to decentration errors of the prisms during assembly. Therefore, it is preferable to increase the number of reflecting surfaces of a single prism, in which the relative positions between the surfaces can be fixed.
Increasing the number of reflecting surfaces of a prism is favorable for performance but may cause the prism to become unfavorably large in size. An optical path cannot freely be folded by using reflecting surfaces. It is generally necessary to fold an optical path so that the effective portions of reflecting surfaces do not overlap each other. For example, when there are a surface a, a surface b, and a surface c in order in which light rays travel, if the angle of reflection at the surface b is excessively small, the effective portions of the surfaces a and c undesirably overlap each other. Therefore, it is necessary to increase the reflection angle at the surface b or to increase the spacing between the surfaces a and b and the spacing between the surfaces b and c so that the effective portions of these surfaces do not overlap each other. Accordingly, as the number of reflecting surfaces increases, the number of restrictions on the direction of reflection and the spacing between reflecting surface increases, and it becomes likely to be difficult to achieve a reduction in size of the prism. Thus, simply increasing the number of reflecting surfaces of the prism is favorable for performance but does not allow achievement of a reduction in size.
Under the above-described circumstances, there has been proposed a method of reducing the size of a prism, in which a transmitting surface and a reflecting surface are formed from the identical surface by using total reflection (such a reflecting surface will hereinafter be referred to as xe2x80x9ca mutual reflecting surfacexe2x80x9d; a reflecting surface that is not formed from the identical surface with a transmitting surface will hereinafter be called xe2x80x9can independent reflecting surfacexe2x80x9d). In this method, a single surface is arranged to refract light when it is transmitted and to totally reflect light when it is reflected, thereby allowing one and the same surface to function as both transmitting and reflecting surfaces. With this arrangement, the effective portions of the reflecting and transmitting surfaces are permitted to overlap each other. Accordingly, the restrictions on the reflection direction and the reflecting surface separation are relaxed, and the prism is unlikely to become large in size even if the number of reflecting surfaces is increased. Thus, it is possible to expect a reduction in size of the prism.
However, it is known that the amount of decentration aberrations produced by a reflecting surface generally increases as the reflection angle at the surface becomes larger. For this reason, if a strong power is given to a mutual reflecting surface, which has a reflection angle larger than the total reflection critical angle, the amount of decentration aberrations produced by the mutual reflecting surface increases unfavorably. Accordingly, a very strong power cannot be given to the mutual reflecting surface, and satisfactory aberration correction cannot be effected. Therefore, the use of a mutual reflecting surface allows a reduction in size but may make it impossible to effect satisfactory aberration correction and hence impossible to attain high performance.
Thus, it has heretofore been difficult in a prism optical system to satisfy the demand for an improvement in performance and the demand for a reduction in size at the same time. Accordingly, the present invention proposes a structure of a compact and high-performance prism optical system attained by optimizing the number of reflections and the arrangement of mutual reflecting surfaces.
As has been stated above, it is important in order to achieve a reduction in size to arrange mutual reflecting surfaces appropriately and also important in order to achieve high performance to increase the number of independent reflecting surfaces used, which allow the reflection angle to be reduced.
It is also important in order to attain a reduction in size to take into consideration the exit direction from the prism optical system. If the exit direction from the prism is set perpendicular or nearly perpendicular to the entrance direction to the prism, it becomes virtually impossible to make the thickness of the optical system smaller than the image height in a case where it is an image-forming optical system. In the case of an ocular optical system, it becomes virtually impossible to make the thickness of the optical system smaller than the height of an intermediate image of a display device or an objective optical system. Accordingly, it is preferable to set the exit direction of the prism parallel or nearly parallel (hereinafter referred to as xe2x80x9capproximately parallelxe2x80x9d) to the entrance direction to the prism. It should be noted that when the exit direction is set approximately parallel to the entrance direction, there are two possible cases, i.e. one in which the direction of travel of emergent rays is the same as the entrance direction, and another in which the travel direction is opposite to the entrance direction. In a case where the travel direction is opposite to the entrance direction, the exit direction is a returning direction with respect to the entrance direction. Therefore, it is necessary to design the optical system so that the effective portions of the first transmitting surface (entrance surface) and the second transmitting surface (exit surface) will not overlap each other. If another member is placed in the vicinity of the exit surface, incident rays may be vignetted. Therefore, it is not preferable to set the travel direction of emergent rays opposite to the entrance direction. Accordingly, it is preferable to arrange the optical system so that the exit direction is the same as the entrance direction.
Therefore, the prism optical system according to the first aspect of the present invention is formed from at least four reflecting surfaces. A first reflecting surface and a fourth reflecting surface are independent reflecting surfaces, and a second reflecting surface and a third reflecting surface are mutual reflecting surfaces. By using independent reflecting surfaces for two of the four reflecting surfaces, it becomes possible to effect satisfactory aberration correction. Further, the second reflecting surface is formed from the identical surface with the first transmitting surface, and the third reflecting surface is formed from the identical surface with the second transmitting surface. With this arrangement, the prism can be effectively reduced in size. Moreover, it becomes easy to set the exit direction of the prism optical system approximately parallel to the entrance direction.
In this case, it is necessary to totally reflect rays at each of the second and third reflecting surfaces. Therefore, it is preferable from the viewpoint of performance to ensure the required power for the prism optical system by giving a power to each of the first and fourth reflecting surfaces, which allow the reflection angle to be made relatively small.
However, because the first and fourth reflecting surfaces are away from each other in terms of the optical path, the ray height in the center of the image field and that at the periphery of the image field differ from each other to a considerable extent. Therefore, if power is given to only the two surfaces, aberrations cannot satisfactorily be corrected because of the difference in ray height. Thus, it is not preferable to give power to only the first and fourth reflecting surfaces.
Therefore, it is necessary in the prism optical system according to the first aspect of the present invention to impart an aberration correcting function, that is, a power, to at least one of the second and third reflecting surfaces, which are placed between the first and fourth reflecting surfaces. With this arrangement, various aberrations can be corrected with good balance. Therefore, it becomes possible to effect aberration correction favorably throughout the image field, from the center to the periphery thereof. Furthermore, it is preferable that at least one of the second and third reflecting surfaces should be formed from a rotationally asymmetric surface.
Accordingly, it is preferable to arrange the prism optical system according to the first aspect of the present invention as follows. The prism optical system comprises at least four reflecting surfaces. When surfaces constituting the prism optical system are defined, in order in which light rays pass from the object side, as a first transmitting surface, a first reflecting surface, a second reflecting surface, a third reflecting surface, a fourth reflecting surface, and a second transmitting surface, the first transmitting surface and the second reflecting surface are formed from the identical surface, and the second transmitting surface and the third reflecting surface are formed from the identical surface. The first reflecting surface and the fourth reflecting surface are formed from surfaces independent of the two transmitting surfaces. Furthermore, a power is given to at least one of the second and third reflecting surfaces. With this arrangement, it becomes possible to obtain a prism optical system that exhibits high performance with a structure smaller in size than the conventional structure.
Next, the prism optical systems according to the second and third aspects of the present invention will be described.
As has been stated with regard to the prism optical system according to the first aspect of the present invention, it is possible to attain a reduction in size and an improvement in performance at the same time by using a rotationally asymmetric surface for a reflecting surface and appropriately arranging reflecting surfaces.
Among optical systems are relay optical systems of the type in which light rays from an object form an image once in the optical path, and the image thus formed is relayed to form a final image. Because it forms an intermediate image, this type of relay optical system generally needs a group of optical elements having strong powers in comparison to an optical system in which an image is not relayed. Therefore, to construct a relay optical system in the prism optical system, the power of each individual surface needs to be increased. If the power of each surface is increased, it may become impossible to correct decentration aberrations satisfactorily even if a rotationally asymmetric surface is used. Therefore, the use of the relay optical system is disadvantageous in terms of performance. In addition, the degree of performance degradation due to surface accuracy errors and decentration accuracy errors increases unfavorably. On the other hand, the relay optical system tends to increase in optical path because it forms an image once in the optical path and relays it. Therefore, if the relay optical system is applied to the prism optical system, the prism becomes undesirably large in size. Thus, the use of the relay optical system, which forms an intermediate image, in the prism optical system is disadvantageous in terms of both performance and size.
In view of these matters, therefore, it is preferable not to form an intermediate image in the prism of the prism optical system according to the present invention. That is, the prism optical system according to the second aspect of the present invention should preferably be arranged so that light rays from an object form an image once only after passing through the second transmitting surface. The prism optical system according to the third aspect of the present invention should preferably be arranged so that light rays from an object are led to the position of an observer""s eyeball only after passing through the second transmitting surface without forming an intermediate image in the prism. It is also preferable that the prism optical system according to the second aspect of the present invention should mainly be used in an image-forming optical system, and the prism optical system according to the third aspect of the present invention should mainly be used in a viewing optical system. It should be noted, however, that when the prism optical system according to the present invention is used in an ocular optical system of a real-image finder, an intermediate image formed by an objective optical system is an object plane of a viewing optical system. With this arrangement, the power of each individual surface need not be made strong. Therefore, the arrangement is advantageous in terms of performance and also allows the prism to be reduced in size.
It is desirable in the prism optical systems according to the second and third aspects of the present invention to impart an aberration correcting function, that is, a power, to at least one of the second and third reflecting surfaces, which are placed between the first and fourth reflecting surfaces. Further, it is preferable that at least one of the second and third reflecting surfaces should be formed from a rotationally asymmetric surface.
Next, the arrangements of the prism optical systems according to the first, second and third aspects of the present invention that can effectively attain the object of the present invention will be described. First, the arrangements of the second and third reflecting surfaces will be described.
It has already been stated that it is necessary to impart an aberration correcting function to either one of the second and third reflecting surfaces of the above-described prism optical systems. Because both the second and third reflecting surfaces totally reflect rays, if either of the reflecting surfaces is given such a large power as required to ensure the power of the prism optical system, the amount of decentration aberrations becomes excessively large, and it becomes impossible to attain high performance. Therefore, it is preferable to give either one of the second and third reflecting surfaces the function of correcting decentration aberrations left uncorrected at the first and fourth reflecting surfaces. Accordingly, it is desirable to form either of the second and third reflecting surfaces from a rotationally asymmetric surface and to arrange the rotationally asymmetric surface so that the curvature thereof in at least either one of X- and Y-axis directions changes from a positive to a negative. This arrangement allows asymmetric aberrations to be corrected favorably.
It is desirable that the curvature in the Y-axis direction of the rotationally asymmetric surface, which changes from a positive to a negative, should satisfy the following condition:
0.01 less than |(CYposxe2x88x92CYneg)/PY| less than 10xe2x80x83xe2x80x83(1)
where CYpos is the positive maximum curvature in the Y-axis direction within the effective surface area; CYneg is the negative maximum curvature in the Y-axis direction within the effective surface area; and PY is the power in the Y-axis direction of the entire prism optical system.
If |(CYposxe2x88x92CYneg)/PY| is not smaller than the upper limit of the condition (1), i.e. 10, asymmetric decentration aberrations are undesirably over-corrected. If |(CYposxe2x88x92CYneg)/PY| is not larger than the lower limit, i.e. 0.01, asymmetric decentration aberrations are undesirably under-corrected.
It is preferable to satisfy the following condition:
0.05 less than |(CYposxe2x88x92CYneg)/PY| less than 3xe2x80x83xe2x80x83(2)
It is desirable that the curvature in the Y-axis direction of the rotationally asymmetric surface, which changes from a positive to a negative, should satisfy the following condition:
0.01 less than |(CXposxe2x88x92CXneg)/PX| less than 10xe2x80x83xe2x80x83(3)
where CXpos is the positive maximum curvature in the X-axis direction within the effective surface area; CXneg is the negative maximum curvature in the X-axis direction within the effective surface area; and PX is the power in the X-axis direction of the entire prism optical system.
If |(CXposxe2x88x92CXneg)/PX| is not smaller than the upper limit of the condition (3), i.e. 10, asymmetric decentration aberrations are undesirably over-corrected. If |(CXposxe2x88x92CXneg)/PX| is not larger than the lower limit, i.e. 0.01, asymmetric decentration aberrations are undesirably under-corrected.
It is preferable to satisfy the following condition:
0.05 less than |(CXposxe2x88x92CXneg)/PX| less than 3xe2x80x83xe2x80x83(4)
It should be noted that both the second and third reflecting surfaces may be formed from surfaces in which the curvature in at least either one of the X- and Y-axis directions changes from a positive to a negative.
Although in the above-described method decentration aberrations are corrected by a reflecting surface in which positive and negative powers are mixed, it is also possible to correct decentration aberrations by distributing powers of different signs, i.e. a positive power and a negative power, to the second and third reflecting surfaces so that the surfaces cancel each other""s aberrations with the powers of different signs. With this arrangement in particular, the first and second transmitting surfaces, which are refracting surfaces identical with the second and third reflecting surfaces, can be given powers of different signs. Therefore, the arrangement is favorable from the viewpoint of chromatic aberration correction.
In this case, it is desirable that the curvatures in the Y-axis direction of the second and third reflecting surfaces should satisfy the following condition:
0.01 less than |(CY2xe2x88x92CY3)/PY| less than 5xe2x80x83xe2x80x83(5)
where CY2 is the curvature at the maximum power in the Y-axis direction within the effective surface area of the second reflecting surface; CY3 is the curvature at the maximum power in the Y-axis direction within the effective surface area of the third reflecting surface; and PY is the power in the Y-axis direction of the entire prism optical system. CY2 and CY3 are the curvatures at points where the powers of the respective surfaces are the maximum. Accordingly, when the power of the reflecting surface is negative, the curvature assumes a negative value. Therefore, in this case, CY2xc2x7CY3 less than 0.
If |(CY2xe2x88x92CY3)/PY| is not smaller than the upper limit of the condition (5), i.e. 5, asymmetric decentration aberrations are undesirably over-corrected. If |(CY2xe2x88x92CY3)/PY| is not larger than the lower limit, i.e. 0.01, asymmetric decentration aberrations are undesirably under-corrected.
It is preferable to satisfy the following condition:
0.05 less than |(CY2xe2x88x92CY3)/PY| less than 2xe2x80x83xe2x80x83(6)
It is desirable that the curvatures in the X-axis direction of the second and third reflecting surfaces should satisfy the following condition:
0.01 less than |(CX2xe2x88x92CX3)/PX| less than 5xe2x80x83xe2x80x83(7)
where CX2 is the curvature at the maximum power in the X-axis direction within the effective surface area of the second reflecting surface; CX3 is the curvature at the maximum power in the X-axis direction within the effective surface area of the third reflecting surface; and PX is the power in the X-axis direction of the entire prism optical system. It should be noted that CX2xc2x7CX3 less than 0.
If |(CX2xe2x88x92CX3)/PX| is not smaller than the upper limit of the condition (7), i.e. 5, asymmetric decentration aberrations are undesirably over-corrected. If |(CX2xe2x88x92CX3)/PX| is not larger than the lower limit, i.e. 0.01, asymmetric decentration aberrations are undesirably under-corrected.
It is preferable to satisfy the following condition:
0.05 less than |(CX2xe2x88x92CX3)/PX| less than 2xe2x80x83xe2x80x83(8)
Next, the arrangements of the first and fourth reflecting surfaces will be described. From the structural point of view of the prism, the first and fourth reflecting surfaces are not restricted in terms of reflection angle. That is, the first and fourth reflecting surfaces need not satisfy the condition for total reflection. Therefore, the amount of decentration aberrations produced by the first and fourth reflecting surfaces can be reduced by setting relatively small reflection angles for these surfaces. If the reflection angle at the first reflecting surface is excessively small, it becomes impossible to effect total reflection of rays at the second reflecting surface, which is a surface subsequent to the first reflecting surface. Accordingly, it is desirable that the reflection angle at the first reflecting surface should satisfy the following condition:
10xc2x0 less than |xcfx861| less than 45xc2x0xe2x80x83xe2x80x83(9)
where xcfx861 is the reflection angle at the first reflecting surface for the axial principal ray.
If |xcfx861| is not smaller than the upper limit of the condition (9), i.e. 45xc2x0, the amount of decentration aberrations produced by this surface becomes unfavorably large, causing the performance to be degraded. If |xcfx861| is not larger than the lower limit, i.e. 10xc2x0, it becomes impossible to effect total reflection of rays at the second reflecting surface.
It is preferable to satisfy the following condition:
15xc2x0 less than |xcfx861| less than 35xc2x0xe2x80x83xe2x80x83(10)
Similarly, because rays are totally reflected at the third reflecting surface, if the reflection angle at the fourth reflecting surface is excessively small, it becomes impossible for rays to pass through the second transmitting surface, which is formed from the identical surface with the third reflecting surface. Therefore, it is desirable that the reflection angle at the fourth reflecting surface should satisfy the following condition:
10xc2x0 less than |xcfx864| less than 45xc2x0xe2x80x83xe2x80x83(11)
where xcfx864 is the reflection angle at the fourth reflecting surface for the axial principal ray.
If |xcfx864| is not smaller than the upper limit of the condition (11), i.e. 45xc2x0, the amount of decentration aberrations produced by this surface becomes unfavorably large, causing the performance to be degraded. If |xcfx864| is not larger than the lower limit, i.e. 10xc2x0, it becomes impossible to effect total reflection of rays at the third reflecting surface.
It is preferable to satisfy the following condition:
15xc2x0 less than |xcfx864| less than 35xc2x0xe2x80x83xe2x80x83(12)
It has already been stated that it is preferable in the prism optical system according to the present invention to give a strong power to each of the first and fourth reflecting surfaces from the viewpoint of ensuring the power required for the prism. Therefore, it is necessary to set the power of the first reflecting surface appropriately to control the amount of decentration aberrations produced by this surface. Accordingly, it is desirable that the curvature in the Y-axis direction of the first reflecting surface should satisfy the following condition:
0.01 less than |CY1/PY| less than 2xe2x80x83xe2x80x83(13)
where CY1 is the curvature at the maximum power in the Y-axis direction within the effective surface area of the first reflecting surface, and PY is the power in the Y-axis direction of the entire prism optical system.
If |CY1/PY| is not smaller than the upper limit of the condition (13), i.e. 2, the power of the first reflecting surface becomes excessively strong, and the amount of decentration aberrations produced by this surface becomes unfavorably large. If |CY1/PY| is not larger than the lower limit, i.e. 0.01, the power of the first reflecting surface becomes excessively weak, and it becomes impossible to correct decentration aberrations.
It is preferable to satisfy the following condition:
0.1 less than |CY1/PY| less than 0.8xe2x80x83xe2x80x83(14)
Similarly, it is desirable that the curvature in the X-axis direction of the first reflecting surface should satisfy the following condition:
0.01 less than |CX1/PX| less than 2xe2x80x83xe2x80x83(15)
where CX1 is the curvature at the maximum power in the X-axis direction within the effective surface area of the first reflecting surface, and PX is the power in the X-axis direction of the entire prism optical system.
If |CX1/PX| is not smaller than the upper limit of the condition (15), i.e. 2, the power of the first reflecting surface becomes excessively strong, and the amount of decentration aberrations produced by this surface becomes unfavorably large. If |CX1/PX| is not larger than the lower limit, i.e. 0.01, the power of the first reflecting surface becomes excessively weak, and it becomes impossible to correct decentration aberrations.
It is preferable to satisfy the following condition:
0.01 less than |CX1/PX| less than 1xe2x80x83xe2x80x83(16)
Similarly, it is necessary to set the power of the fourth reflecting surface appropriately. Accordingly, it is desirable that the curvature in the Y-axis direction of the fourth reflecting surface should satisfy the following condition:
0.01 less than |CY4/PY| less than 2xe2x80x83xe2x80x83(17)
where CY4 is the curvature at the maximum power in the Y-axis direction within the effective surface area of the fourth reflecting surface, and PY is the power in the Y-axis direction of the entire prism optical system.
If |CY4/PY| is not smaller than the upper limit of the condition (17), i.e. 2, the power of the fourth reflecting surface becomes excessively strong, and the amount of decentration aberrations produced by this surface becomes unfavorably large. If |CY4/PY| is not larger than the lower limit, i.e. 0.01, the power of the fourth reflecting surface becomes excessively weak, and it becomes impossible to correct decentration aberrations.
It is preferable to satisfy the following condition:
0.1 less than |CY4/PY| less than 0.8xe2x80x83xe2x80x83(18)
Similarly, it is desirable that the curvature in the X-axis direction of the fourth reflecting surface should satisfy the following condition:
0.01 less than |CX4/PX| less than 2xe2x80x83xe2x80x83(19)
where CX4 is the curvature at the maximum power in the X-axis direction within the effective surface area of the fourth reflecting surface, and PX is the power in the X-axis direction of the entire prism optical system.
If |CX4/PX| is not smaller than the upper limit of the condition (19), i.e. 2, the power of the fourth reflecting surface becomes excessively strong, and the amount of decentration aberrations produced by this surface becomes unfavorably large. If |CX4/PX| is not larger than the lower limit, i.e. 0.01, the power of the fourth reflecting surface becomes excessively weak, and it becomes impossible to correct decentration aberrations.
It is preferable to satisfy the following condition:
0.1 less than |CX4/PX| less than 1xe2x80x83xe2x80x83(20)
It is preferable from the viewpoint of aberration correction to distribute powers of the same sign to the first and fourth reflecting surfaces. If the prism optical system is arranged so that all the surfaces have negative powers, the prism becomes undesirably large in size because the light beam diverges. Accordingly, it is not always possible to attain a reduction in size even if the optical axis is folded by using reflecting surfaces. Therefore, it is preferable to give positive powers to both the first and fourth reflecting surfaces.
It has been stated in the foregoing that setting the optical axis entering the prism optical system and the optical axis exiting therefrom approximately parallel to each other is effective in achieving a reduction in size. It is most desirable that the entering and exiting optical axes should be completely parallel to each other. However, because of the necessity of providing another member, it is not always possible to attain a reduction in size if the entering and exiting optical axes are set completely parallel to each other. Accordingly, it is desirable that the axial principal ray entering the prism optical system and the axial principal ray exiting therefrom should satisfy the following condition:
0xc2x0xe2x89xa6xcex8 less than 45xc2x0xe2x80x83xe2x80x83(21)
where xcex8 is the angle formed between the axial principal ray entering the prism optical system and the axial principal ray exiting therefrom.
If the angle xcex8 is not smaller than the upper limit of the condition (21), i.e. 45xc2x0, the thickness of the prism in the direction of the optical axis entering the prism optical system becomes undesirably large, and it becomes impossible to attain a reduction in size.
It is preferable to satisfy the following condition:
0xc2x0xe2x89xa6xcex8 less than 20xc2x0xe2x80x83xe2x80x83(22)
where xcex8 is the angle formed between the axial principal ray entering the prism optical system and the axial principal ray exiting therefrom.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification.
The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims.